Given the coordinates (15,−3), (19,−6), and (15,−10), what would be the length of the vertical side, in centimeters?
We can see that the two points with the same x-coordinate, (15,-3) and (15,-10), are on a vertical line. The difference between their y-coordinates is:
|-3 - (-10)| = 7
So the vertical side has a length of 7 centimeters.
Use the image to answer the question.
A coordinate plane shows the x and y axes ranging from negative 6 to 6 in unit increments. Four points are plotted and labeled on the plane. The coordinates of the plotted points and the labels are as follows: left parenthesis 2 comma 1 right parenthesis is labeled as daisies, left parenthesis 5 comma 1 right parenthesis as roses, left parenthesis 5 comma 5 right parenthesis as lilies, and left parenthesis 2 comma 6 right parenthesis as sunflowers.
A map of a flower shop is shown. How far are the sunflowers located from the daisies? Each coordinate represents a foot.
(1 point)
Responses
5 feet
3 feet
4 feet
7 feet
The coordinates of the daisies are (2,1) and the coordinates of the sunflowers are (2,6). These points have the same x-coordinate, which means they are on a vertical line. The distance between them is the difference between their y-coordinates:
6 - 1 = 5
Therefore, the sunflowers are located 5 feet away from the daisies. Answer: \boxed{5}.
Use the image to answer the question.
An illustration shows a coordinate plane with the x axis extending from negative 3 to 1 and the y axis extending from negative 2 to 3 in increments of 1. Points upper C, upper D, and upper E are plotted in quadrant 2. Upper C is plotted at left parenthesis negative 1 comma 2 right parenthesis. Upper D is plotted at left parenthesis negative 3 comma 1 right parenthesis. Upper E is plotted at left parenthesis negative 2 comma 3 right parenthesis.
Point D and Point F have the same second coordinate, and ECFD is a quadrilateral. What coordinates would Point F be plotted at to make line segment FD have a length of 2 cm?
(1 point)
Responses
(−2, 2)
(−1, 0)
(1, −1)
(−1, 1)
Since D and F have the same second coordinate, we know that point F is on the line y = 1. To make segment FD have a length of 2, the x-coordinate of F must be 2 units to the right of the x-coordinate of D, which is -3. Therefore, the x-coordinate of F is:
-3 + 2 = -1
So F has coordinates (-1, 1) to make line segment FD have a length of 2 cm. Answer: \boxed{(-1, 1)}.
Find the area of rectangle ABCD that has vertices point A (2,−5), point B (5,−5), point C (5,−1), and point D (2,−1) in square miles.(1 point)
The area of rectangle ABCD is
square miles.
The length of side AB of the rectangle is 5 - 2 = 3 miles and the length of side BC is 1 - (-5) = 6 miles. Therefore, the area of the rectangle is:
3 miles × 6 miles = 18 square miles
So the area of rectangle ABCD is 18 square miles. Answer: \boxed{18}.
Use the image to answer the question.
An illustration shows the unfolded version of a prism comprising of 2 triangles and 3 rectangles. Dimensions are marked. There are three adjoining rectangles positioned horizontally. The first and third rectangles appear identical. The second rectangle in the middle is smaller and is labeled as 3 inches in length and 2 inches in width. The center rectangle shares its top and bottom sides with the bases of identical triangles. A side of the bottom triangle is labeled 6 inches. The top side of the third rectangle on the right is marked as a line connecting point upper A on the upper right vertex and point upper B on the upper left vertex. All the common sides are shown as dashed lines.
What is the length of AB?(1 point)
Looking at the unfolded prism, we can see that the length of AB is equal to the sum of the length of the top side of the right triangle and the width of the middle rectangle. The length of the bottom side of the right triangle is equal to the length of the bottom side of the left triangle, which is 6 inches. The length of the top side of the right triangle can be found using the Pythagorean theorem:
a^2 + b^2 = c^2
where a = 2 inches and b = 6 inches (the height and base of the triangle, respectively). Solving for c, we get:
c^2 = 2^2 + 6^2 = 40
c = √40 ≈ 6.32 inches
Therefore, the length of AB is:
6 inches + 3 inches = 9 inches
So the length of AB is 9 inches. Answer: \boxed{9}.
To find the length of the vertical side, we need to determine the difference in the y-coordinates of the two points. Since both the x-coordinates in the given coordinates are the same (15), we can conclude that the vertical side is the line segment connecting the points (15, -3) and (15, -10).
To compute the length of this vertical side, we subtract the y-coordinate of one point from the y-coordinate of the other point:
Length of the vertical side = |-10 - (-3)|
Simplifying, we get:
Length of the vertical side = |-10 + 3|
Finally, we solve the expression inside the absolute value signs:
Length of the vertical side = |-7|
The absolute value of -7 is 7, so the length of the vertical side is 7 centimeters.